NC0003468_7. DRSS_CAP Part 2_Appx D_FINAL_20160210

Appendix D
Surface Water Mixing
Model Approach

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Surface Water Mixing Model Approach
Dan River Steam Station
Overview of Modeling
The relatively simple morphology of receiving waters adjacent to Dan River Steam Station
(DRSS) makes the site amenable to the mixing model approach. For this approach, river flow
data from the U.S. Geological Survey (USGS) were analyzed to determine upstream river
design flows and assess compliance with North Carolina Department of Environmental Quality
surface water quality standards, including determination of 1Q10, 7Q10, and mean annual river
flows. The 1Q10 flow is the annual minimum 1-day average flow that occurs once in 10 years;
the 7Q10 flow is the annual minimum 7-day average flow that occurs once in 10 years; and the
mean annual flow is the long-term average annual flow based on complete annual flow records.
The river discharge design flows were combined with groundwater model discharge results to
calculate effluent dilution factors using the following equation:
𝐷𝐷𝐷𝐷=𝑄𝑄𝑔𝑔𝑔𝑔+𝑄𝑄𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑄𝑄𝑔𝑔𝑔𝑔
where: DF is the groundwater dilution factor;
Qgw is discharge rate from the groundwater model (cubic feet per second [cfs]);
and
Qriver is the upstream river design flow (cfs).
The mixing zone sizes presented in Section 4.2 of the Corrective Action Plan (CAP) Part I
Report for the different water quality standards were used in this equation to determine the
appropriate dilution factor to assess compliance with the applicable water quality standards. The
applicable dilution factor was then used with the groundwater model concentration and
upstream concentration for the constituent of interest (COI) to determine the resulting surface
water concentration at the edge of the mixing zone using the following equation:
𝐶𝐶𝑠𝑠𝑠𝑠=(𝐷𝐷𝐷𝐷−1)×𝐶𝐶𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟+𝐶𝐶𝑔𝑔𝑔𝑔𝐷𝐷𝐷𝐷
where: Csw is the surface water concentration at the edge of the mixing zone
(micrograms per liter [µg/L]);
Cgw is the groundwater model concentration entering the river (µg/L);
Criver is the upstream (background) river concentration (µg/L); and
DF is the groundwater dilution factor.

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Surface Water Mixing Model Approach
Dan River Steam Station Ash Basin

Alternately, the resulting surface water concentration can be calculated using the following mass
balance equation:
𝐶𝐶𝑠𝑠𝑠𝑠=𝑄𝑄𝑔𝑔𝑔𝑔×𝐶𝐶𝑔𝑔𝑔𝑔+𝑄𝑄𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟×𝐶𝐶𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑄𝑄𝑔𝑔𝑔𝑔+𝑄𝑄𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟𝑟
where: Qgw is discharge rate from the groundwater model (cfs);
Cgw is the groundwater model concentration entering the river (µg/L);
Qriver is the upstream river design flow (cfs); and
Criver is the upstream (background) river concentration (µg/L).

For each groundwater COI that discharges to surface waters at a concentration exceeding the
North Carolina Groundwater Quality Standards, as specified in T15A NCAC .0202L (2L
Standards), the appropriate dilution factor and upstream (background) concentration were
applied to determine the surface water concentration at the edge of the applicable mixing zone.
This concentration was then compared to the applicable water quality standards to determine
surface water quality standard compliance.
Historical USGS river flow data are available for the Dan River near Wentworth, NC (Gage
#02071000, 1939 to present), which is located approximately 14 miles upstream of the DRSS.
The only major tributary to the Dan River over this section is the Smith River, which enters the
Dan River approximately 3 miles upstream of the DRSS and (USGS Gage #02074000, 1939 to
present). Daily river flow data from these two gages were summed and analyzed to calculate
1Q10, 7Q10, and mean annual design flows for the Dan River at the DRSS.
Key Assumptions and Limitations for Each Model
The key model assumptions and limitations include, but are not limited to, the following:
• Groundwater flow mixing in the receiving water occurs over the entire cross-section of
the mixing zone area (e.g., over 10% of the river width for the acute water quality
assessment).
• COI transformations are not represented in the analysis (i.e., all COIs are treated as
conservative substances without any decay).
• The analysis is limited by the availability of surface water data used to assign upstream
river COI concentrations.
Mixing Model Development
The mixing model approach requires the assignment of upstream critical river design flows for
the fraction of the river as specified in Section 4.2 of the CAP Part I Report for the acute,
chronic, and human health mixing zone limitations. The 1Q10, 7Q10, and mean annual river
design flows were calculated from the sum of flows at the Dan River near Wentworth and Smith
River, as presented in Table 1.
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Surface Water Mixing Model Approach
Dan River Steam Station Ash Basin

Table 1 Dan River Design Flows
Design Condition Design Flow (cfs)
1Q10 264
7Q10 382
Mean Annual 1,817

For the water quality assessment in the unnamed east tributary, it was assumed that the
upstream low flow was negligible and the resulting surface water concentration was equal to the
groundwater model calculated concentration entering the tributary. There were limited flow
measurements on the east tributary from August 6, 2015 that averaged 0.1 cfs, which indicates
that the mixing model approach taken here is conservative.
In addition, dissolved groundwater COI concentrations entering the unnamed east tributary and
unnamed east tributary surface water dissolved COI concentrations are required, which were
determined from observed site monitoring data. Table 2 lists these concentrations and also
provides the applicable North Carolina Department of Environmental Quality or U.S.
Environmental Protection Agency surface water quality standards. Groundwater and surface
water data from the Dan River are provided in Table 3.
Table 2 Unnamed East Tributary Dissolved COI Concentrations and Water Quality
Standards
COI
Groundwater
Concentration
(µg/L)
Surface Water
Concentration
(µg/L)*
Acute WQS
(µg/L)
Chronic
WQS (µg/L)
Human
Health WQS
(µg/L)
Arsenic 0.956 11.3 340 150 10
Boron 48.2 97.1 ns ns ns
Total Chromium 4.73 4.62 ns ns ns
Hexavalent
Chromium 0.084 0.021 16 11 ns
Cobalt 0.483 0.618 ns ns 4
Sulfate 13,125 14,425 ns ns ns
Thallium 0.193 0.125 ns ns 0.47
Vanadium 0.948 0.856 ns ns ns
Notes:
1. All COIs are shown as dissolved except for total chromium
2. * – average of data from site stations SW-3, SW -4, SW -10, SW -11, SW -12 and SW-13
3. WQS = water quality standard
4. ns = no water quality standard
5. Human Health / Water Supply (15A NCAC 02B .0211, 15A NCAC 02B .0216, effective January 1, 2015)

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Surface Water Mixing Model Approach
Dan River Steam Station Ash Basin

Table 3 Dan River Dissolved COI Concentrations and Water Quality Standards
COI
Groundwater
Concentration
(µg/L)
Surface Water
Concentration
(µg/L)*
Acute WQS
(µg/L)
Chronic
WQS (µg/L)
Human
Health WQS
(µg/L)
Arsenic 1.24 0.235 340 150 10
Boron 263 150 ns ns ns
Total Chromium 3.32 0.500 ns ns ns
Hexavalent
Chromium 0.061 0.500** 16 11 ns
Cobalt 0.332 0.465 ns ns 4
Sulfate 35,994 5,150 ns ns ns
Thallium 0.133 0.059 ns ns 0.47
Vanadium 0.868 1.65 ns ns ns
Notes:
1. All COIs are shown as dissolved except for total chromium
2. * – Data from upstream site station SW -8
3. ** – Value set equal to total chromium value
4. ns = no water quality standard
5. Human Health / Water Supply (15A NCAC 02B .0211, 15A NCAC 02B .0216, effective January 1, 2015)
The groundwater concentrations presented in the Tables 2 and 3 are based on model output
from the groundwater model developed for the DRSS. It should be noted that all of the
measured surface water concentrations in the unnamed east tributary and in the Dan River are
less than the associated water quality standard except for two arsenic measurements in the
unnamed east tributary at stations SW-3 and SW -10 that are greater than the human health
water quality standard.
In addition, the acute and chronic water quality standards for arsenic and hexavalent chromium
use a water effects ratio of 1, which expresses the difference between the laboratory- measured
toxicity and toxicity in site water. Measured water effects ratios are typically less than 1 due to
complexing parameters in the site water (e.g., dissolved organic carbon) that reduce the site
toxicity as compared to laboratory measured toxicity for metals. Therefore, use of a water
effects ratio of 1 provides a conservative assumption in the surface water quality assessment.
Groundwater modeling discussed in Section 4.1 of the CAP Part I Report was used to provide
the groundwater flow and COI concentrations into the adjacent receiving waters (unnamed
tributary to the east of the DRSS and the Dan River). Figure 1 depicts the location of the
groundwater model calculated flow inputs into these adjacent receiving waters, and Table 4
provides the total flow along the two flow paths noted in Figure 1. These groundwater flows
were used to assess the impact on surface water concentrations and compliance with the
applicable water quality standards at the mixing zone boundaries in the unnamed east tributary
and the Dan River.

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Surface Water Mixing Model Approach
Dan River Steam Station Ash Basin

Table 4 Model-Calculated Groundwater Flows
Waterbody Groundwater Flow
(ft3/day) (cfs)
Unnamed East Tributary 571 0.0066
Dan River (Total) 21,900 0.2535
Notes:
1. ft3/day = cubic feet per day

The values reported in the preceding tables were used to calculate the COI concentrations in the
unnamed east tributary (completely mixed) and in the Dan River at the mixing zone boundaries
for comparison to the applicable water quality standards to assess water quality compliance of
the groundwater discharges from the DRSS.

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Surface Water Mixing Model Approach
Dan River Steam Station Ash Basin

Figure 1 DRSS Groundwater Model Flow Locations and Surface Water Stations

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